A&A 521, A60 (2010) Astronomy DOI: 10.1051/0004-6361/201014486 & c ESO 2010 Astrophysics

Planetary transit timing variations induced by stellar binarity The light travel time effect

M. Montalto1,2

1 Max-Planck-Institute for Extraterrestrial Physics, Giessenbachstr., 85741 Garching b. Muenchen, Germany 2 Universitaetssternwarte Muenchen, Scheiner Str. 1, 81679 Muenchen, Germany e-mail: [email protected] Received 23 March 2010 / Accepted 15 June 2010

ABSTRACT

Context. Since the discovery of the first transiting extrasolar planet, transit timing has been recognized as a powerful method to discover and characterize additional planets in these systems. However, the gravitational influence of additional planets is not the only expected source of transit timing variations. Aims. In this work, we derive the expected detection frequency of stellar companions of hot-jupiter transiting planets host-, detectable by means of transit timing analysis. Since roughly half of the stars in the solar neighborhood belong to binary or multiple stellar systems, the same fraction of binary systems may be expected to be present among transiting planet-host stars, unless planet formation is significantly influenced by the presence of a stellar companion. Transit searches are less affected by the selection biases against long-period binaries that plague surveys. Methods. We considered the frequency and the period, ratio and eccentricity distributions of known binary systems in the solar neighborhood, and estimated the fraction of transiting planet-hosts expected to show detectable transit timing variations due to the light travel time effect in a binary stellar system, in function of the time since the discovery of the planet. Results. If the frequency of binaries among hot-jupiter planet host stars is the same as determined in the solar neighborhood, after 5 since the discovery of a sample of transiting planets 1.0% ± 0.2% of them have a probability >99% to present transit timing variations >50 s induced by stellar binarity, and 2.8% ± 0.3% after 10 years, if the planetary and binary orbits are coplanar. Considering the case of random inclinations the probabilities are 0.6% ± 0.1% and 1.7% ± 0.2% after 5 and 10 years respectively. Our estimates can be considered conservative lower limits, since we have taken into account only binaries with periods P > 5 × 103 days (a ∼> 6AU). Our simulations indicate that transit timing variations due to the light travel time effect will allow us to discover stellar companions up to maximum separations equal to a ∼ 36 AU after 5 years since the discovery of the planet (a ∼ 75 AU after 10 years). Conclusions. Comparing the results of the observations with the above predictions allows to understand if stellar companions at critical separations (<100 AU) are favoring or hindering the formation of hot-jupiter planets. Comparing the results of transit timing detections with those obtained by other complementary methods results in a more complete determination of stellar multiplicity around transiting planet-host stars. Moreover, transit timing analysis allows us to probe stellar multiplicity at critical separations (<100 AU) around stars located in different regions of the , and not just in the solar neighborhood. Key words. time – ephemerides – occultations – binaries: general

1. Introduction ∼50 AU, both by means of the disk instability (Boss 1997)and the core accretion mechanisms (Pollack et al. 1996). On the con- The frequency of binary stars and multiple stellar systems trary Boss (2006), showed that in the context of the disk insta- around solar-like stars in the solar neighborhood has been ex- bility scenario, the presence of a close-by stellar companion may tensively studied in the past. Duquennoy & Mayor (1991), from in fact trigger clumps formation leading to giant planets. Along a sample of 164 primary G-dwarf stars analyzed during almost the same lines Duchêne (2010) suggested that in tight binaries 13 yr with the CORAVEL spectrograph, obtained that the ratios (a < 100 AU) massive planets are formed by disk instability at of single:double:triple:quadruple systems are 51:40:7:2 respec- the same rate as less massive planets in wider binaries and single tively. This fraction of binaries should be present also in a sam- stars. ple of planet host stars if planets do form in any kind of binary According to Marzari et al. (2005), independently from the systems and there are no selection biases applied to define the planet formation mechanism, tidal perturbations of the compan- sample of stars where the planets are searched for. ion influence both the onset of instability and the following From a theoretical point of view the problem of the forma- chaotic evolution of protoplanetary disks. In particular several tion of giant planets in close binary systems is still largely de- studies have pointed out that the gravitational influence of stel- bated. Truncation and heating of circumstellar protoplanetary lar companions on the dynamics of planetary systems becomes disks are expected to occur in close binary systems (Artymowics significant at separations ≤100 AU (e.g. Pfhal & Muterspaugh & Lubow 1994;Nelson2000). However there is no general con- 2006; Desidera & Barbieri 2007; Duchêne 2010). Despite that, sensus on which consequences these processes have on planet four planetary systems have been discovered in binaries with formation. Nelson (2000) showed that the formation of giant separations around 20 AU: Gamma Cephei (Hatzes et al. 2003), planets is unlikely in equal mass binaries with semi-major axis Gliese 86 (Queloz et al. 2000; Els et al. 2001), HD 41004 Article published by EDP Sciences Page 1 of 6 A&A 521, A60 (2010)

(Santos et al. 2002), and HD 196885 (Correia et al. 2008). These planets with Rossiter-McLaughlin measurements, Triaud et al. observational results are clearly challenging our current knowl- (2010) derived that most transiting planets have misaligned or- edge of planet formation and evolution in binary systems. bits (80% with ψ>22◦), and that the histogram of projected Several imaging surveys have successfully identified stel- obliquities closely reproduces the theoretical distribution of ψ lar companions to planet-host stars (e.g. Patience et al. 2002; using Kozai cycles and tidal friction (Fabrycky & Tremaine Luhman & Jayawardhana 2002; Chauvin et al. 2006; Mugrauer 2007). Since type I and II migration are not able to explain the et al. 2007; Eggenberger et al. 2007; Eggenberger & Udry 2007). present observations, the indication is that the Kozai mechanism At present, giant planets around wide binary systems appear as is the major responsible of the formation of hot-jupiter planets. frequent as planets around single stars (Bonavita & Desidera In this case, we should expect that most hot-jupiter planets have 2007), suggesting that wide binaries are not significantly altering stellar companions. The discovery of close stellar companions to planet formation processes. However, there is a marginal statisti- transiting planets systems is then of primary importance, since cal evidence that binaries with separations smaller than 100 AU it would constitute a strong proof in favor of the Kozay cycles may have a lower frequency of planetary systems than around and tidal friction mechanism. Transiting planets host stars then single stars. Eggenberger et al. (2008) estimated a difference in constitute an interesting sample of objects where to look for ad- the binary frequency between carefully selected samples of non ditional distant companions. The presence of a stellar compan- planet-host and planet-host stars ranging between 8.2% ± 5.0% ion around these stars can be inferred at least by means of four and 12.5% ± 5.9%, considering binaries with semi-major axis independent and complementary techniques: transit timing vari- between 35 AU and 250 AU, further pointing out that this dif- ations, radial velocity drifts, direct imaging and IR excess. ference seems mostly evident for binaries with a < 100 AU. Deriving the expected f requency of transiting planet host These results are obtained using samples of stars hosting radial stars in binary stellar systems detectable by each one of the velocity discovered planets, for the obvious reason that Doppler above mentioned techniques is then important, since compar- spectroscopy has been so far the most successful planet detection ing the results of the observations with the predictions we can method, providing then the largest sample of planets from which better understand which influence close binary systems have on statistical conclusions can be drawn. Nevertheless, planets dis- planet formation and evolution. If, for example, the existence of covered with this technique are known to be adversely selected hot-jupiters is connected to the presence of close-by stellar com- against close binaries. Doppler spectroscopy is complicated by panions, we should expect to derive a higher binary frequency light contamination of stellar companions, and blending of spec- around stars hosting these planets, with respect to the frequency tral lines. This implies that radial velocity surveys typically ex- of binaries observed in the solar neighborhood. If, on the con- clude known moderately and close binaries from their target trary, the presence of close-by stellar companions strongly pre- lists. As a consequence the occurrence of planetary systems in vents the existence of planets, we should expect a lower fre- binaries, and in particular at critical separations (≤100 AU), quency. In this paper we focus our attention on transit timing is still poorly constrained by the observations. While the use of variations (TTVs) induced by stellar binarity. Future contributes a control sample of stars, proposed by Eggenberger et al. (2007, will account for the other techniques. 2008), is expected to mitigate the impact on the results given In particular here we derive the expected f requency of tran- by the bias against close binaries applied by radial velocity sur- siting planets in binary systems detectable by TTVs. We define veys, other samples of planet-host stars and different techniques the detection f requency ( fdet) as the fraction of transiting plan- may be useful to probe the frequency of planets in binary stellar ets expected to show detectable TTVs induced by stellar binarity systems. over some fixed timescales, when the only source of TTVs un- While radial velocity planet searches tend to exclude binaries der consideration is the light travel time effect in binary systems. from their target lists, transit searches do not apply a priori se- The presence of an additional stellar companion around a tran- lection criteria against binaries. Transiting planets are routinely siting planet-host star, should induce TTVs even if we neglect searched among all stars, and then subjected to follow-up pho- perturbing effects, because of the variable distance of the host tometric and spectroscopic analysis. Photometric analysis aims star with respect to the observer in the course of its orbital rev- mainly at ruling out grazing eclipsing binary stellar systems olution around the barycenter of the binary stellar system. This which manifest themselves by means of markedly V-shaped motion induces TTVs affecting the observed period of the tran- eclipses, the presence of secondary eclipses, color changes dur- siting object, and consequently the ephemerides of the transits ing the eclipses and light modulations with the same periodicity (e.g. Irwin 1959). of the transiting object. Spectroscopic analysis is then used to Transit timing allows detenction of close stellar compan- further rule-out giant stars primaries and the more complicated ions around more distant planet-host stars than direct imag- scenarios involving hierarchical triple systems with an eclips- ing. Accurate transit timing measurements are achievable also ing binary stellar system, and blends with background eclipsing for planets discovered around faint and distant planet-hosts, by binaries (Brown 2003). However, these follow-up analysis do means of a careful choice of the telescope and the detector not eliminate planets in binary stellar systems. Several transiting (e.g. Adams et al. 2010). On the contrary, the distance of the planets are already known members of binaries (e.g. Daemgen planet-host constitutes a limit for direct imaging detection of et al. 2009), and others have suspected close companions as stellar companions. Using VLT/NACO, and targeting solar type indicated by the presence of radial velocity and transit timing close-by stars (∼10 pc), a companion with a mass of 0.08 M variations (Winn et al. 2010;Maxtedetal.2010;Quelozetal. (then just at the limit of the regime) can be de- 2010; Rabus et al. 2009). Moreover for transiting planets we tected at the 3-σ limit at a projected separation of 0.3 arcsec have a firm constraint on the planetary (which (e.g. Schnupp et al. 2010; Eggenberger et al. 2007), which cor- is close to 90◦). The Rossiter-McLaughlin effect (Rossiter 1924; responds to 3 AU. If, however, the star is located at a distance McLaughlin 1924) can be used to probe the sky-projected an- >333 pc, direct imaging can probe only separations >100 AU. gle β between the axis and the planet’s orbital Then transit timing allows us to probe stellar multiplicity at crit- axis. By transforming the projected angle β into the the real spin- ical separations <100 AU (as demonstrated in this work) around orbit angle ψ using a statistical approach and the entire sample of more distant samples of transiting planet host-stars with respect

Page 2 of 6 M. Montalto: Planetary transit timing variations induced by stellar binarity to what can be done by direct imaging, giving the opportunity and given also that our adopted observing window (10 years) is to probe stellar multiplicity around targets located in different smaller than the shortest period we considered, the perturbing regions of the Galaxy. Moreover, while direct imaging is more effects of the secondary star on the orbit of the inner planet can efficient in detecting companions in face-on orbits, transit tim- be neglected1. The three body problem can be splitted in two in- ing (and Doppler spectroscopy) is more efficient in the case of dependent two body problems: the motion of the planet around edge-on systems. the host star (which can be reasonably assumed coincident with This paper is organized as follows: in Sect. 2,wereview the barycenter of the planetary system given that the mass of the the known properties of binary stellar systems in the solar planet is much smaller than the mass of the star), and the motion neighborhood; in Sect. 3, we discuss the light travel time ef- of the host star around the barycenter of the binary system. Even fect of transiting planets in binaries; in Sect. 4, we describe neglecting perturbing effects, we expect transit timing variations the Monte Carlo simulations we did to constrain the frequency to be present, due to the light travel time effect, as described in of transiting planet-host stars presenting detectable transit tim- Sect. 1. The transiting planet can be used as a precise clock un- ing variations induced by binarity over some fixed timescales; veiling the presence of the additional star in the system. in Sect. 5, we discuss the results of our analysis; in Sect. 6,we We consider a reference system with the origin in the summarize and conclude. barycenter of the binary system. The Z axis is aligned along the line of sight, the X axis along the nodal line defined by the intersection between the binary orbital plane and the plane of 2. Properties of multiple stellar systems the sky, and the Y axis consequently assuming a right-handed From their study of multiple stellar systems in the solar neigh- Cartesian coordinate system. The XY-plane is tangent to the ce- borhood, Duquennoy & Mayor (1991) derived the following lestial sphere. properties for binary stellar systems with mass ratios q > 0.1: The distance (z) between the host star and the barycenter of 1) the distribution can be approximated by: the binary system, projected along the observer line of sight is given by (e.g. Kopal 1959): − − 2 = (log P log P) f (log P) C exp (1) a (1 − e2) 2σ2 z = 1 sin(ω + f )sin(i), (3) log P 1 + e cos( f ) P = . σ = . P where log 4 8, log P 2 3, and is in days; where the orbital elements are relative to the barycentric or- P > 2) binaries with periods 1000 days (which is the range of bit of the host star. Using the equation of the center of mass periods in which we are interested, see below) have an observed a = m a/(m + m ), the Kepler law and dividing by the speed eccentricity distribution which tends smoothly toward h(e) = 2e; 1 2 1 2 of light (c), gives: 3) the mass-ratio (q = m2/m1) distribution can be approxi- mated by: (G)1/3 P2/3(1 − e2) m sin(i) sin(ω + f [t]) O(t) = 2 , (4) 2 2/3 2/3 −(q − q) c (2π) (m1 + m2) 1 + e cos( f [t]) g q = k ( ) exp 2 (2) 2σq where f is the true anomaly, e is the eccentricity of the orbit, and i is the inclination with respect to the plane of the sky, m1 and where q = 0.23, σq = 0.42, k = 18 for their G-dwarf sample. In the following we will consider only binaries with periods m2 are the of the primary and of the secondary, ω is the P > 5 × 103 days. This limit is due to the need to minimize argument of the pericenter, P is the period, G the gravitational perturbing effects, which have been explicitely neglected in our constant, t the of observation, and we just recall that the analysis, as explained in Sect. 3. orbital elements are relative to the binary orbit. Using the period distribution of Duquennoy & Mayor Equation (4) gives the time necessary to cover the distance (1991), we have that ∼68% of all binary systems are expected projected along the line of sight between the host star and the × 3 barycenter of the binary system at the speed of light. We can to have P > 5 10 days and, considering that the frequency of ff binary stellar systems in the solar neighborhood is 40% (as re- also say that Eq. (4) gives the di erence between the observed portedinSect.1, excluding multiple stellar systems), we have ephemerides of the transiting planet once including the light time effect and the ephemerides obtained considering the intrinsic pe- that the expected frequency of binaries in our period range is 2 equal to 68% · 40%  27%. riod of the planet . The aim of the rest of this paper is to establish how many of The rate of change over time of the observed planet period these systems should appear as detectable transit timing sources with respect to the intrinsic planet period is given by the deriva- over a timescale of at most 10 years since the discovery of the tive of Eq. (4) over time: transiting planets around the primary stars of these systems.   (2π)1/3 (G)1/3m sin(i) (t)= √ 2 cos(ω+ f [t])+e cos(ω) . (5) cP1/3 1−e2 (m +m )2/3 3. The light travel time effect 1 2 The procedure usually adopted by observers to determine the In the following we consider the case of a planet orbiting the pri- period of a transiting object is based on the determination of mary star of a binary stellar system. This configuration is usually the time interval between two or more measured transits at an called S-type orbit. We will also assume that the planet is re- epoch t .Then(t ) =  can be seen as the difference between volving much closer to its parent star than the companion star 0 0 0 the observed and the intrinsic period at the observed time t0 (Pbin  Ppl where Pbin is the binary orbital period, and Ppl is the planet orbital period). This is a reasonable assumption given the 1 In particular secular perturbations, see e.g. Kopal (1959)foradis- 3 range of binary periods we are considering (Pbin > 5 × 10 days, cussion of perturbing effects of a third body on a close eclipsing binary. see above), and that most transiting planets are typically hot- 2 We are assuming that the barycentric radial velocity of the binary jupiters with a period of only a few days. Under this assumption, stellar system is γ = 0.

Page 3 of 6 A&A 521, A60 (2010) due to light time effect; to avoid accumulation of this difference over time in the ephemeris it needs to be subtracted. Figure 1 (upper figure, upper panel, dotted line) shows this accumula- tion with time. The difference between the observed and the predicted ephemerides (O−C) of successive transits at another generic epoch (characterized by the binary true anomaly f and the epoch t = t0 +Δt), is then given by:

[O−C](t) = O(t) − O(t0) − 0 (t − t0). (6) Imposing that the O−C residual is larger than a given detection threshold τ is equivalent to solve the following disequation:

| O(t0 +Δt) − O(t0) − 0 (Δ t) |−τ>0. (7) In Fig. 1 (upper figure), we present an illustrative example. We consider a binary system where the relevant orbital elements were fixed at the median values derived by Duquennoy & Mayor (1991): Pbin = 172.865 years, e = 0, q = m2/m1 = 0.23, ω = 0, i = 90◦. We assume that a planet is orbiting the primary star of the binary system, and that the period of the planet was measured at the epoch t0 (assumed coincident with the origin of the x-axis in Fig. 1). After five years the transit timing variation is 46 s, and after ten years it is 178 s, as shown in the inner plot of Fig. 1. The binary we have considered is one of the typical binaries in the solar surrounding. We also observe that the O−C diagram is in general not periodic as evident already from Fig. 1.

4. Simulations In this section we describe the orbital simulations we did to con- strain the expected frequency of transiting planet-host stars that should present a detectable transit timing variation induced by stellar binarity over a timescale of 5 years and 10 years since the discovery of the planet around the primary star of the system. The detectability threshold was fixed considering the results ob- tained by transit timing searchers with ground based telescopes. Rabus et al. (2009), observing the planetary system TrES-1 with the IAC80 cm telescope obtained mean precisions of 18.5 s, which is also in agreement with the theoretical equation given by Doyle & Deeg (2004). On the basis of that, and using sev- eral other literature results, they were already able to claim the presence of a linear trend equivalent to 48 s (obtained from their best-fit parameter) over the period of 4.1 yr spanned by the en- tire sample of the observations. Winn et al. (2009) measured two Fig. 1. Upper figure, upper panel: the black solid curve represents the difference between the observed transit ephemerides of the planet once transits of the WASP-4b with the Baade 6.5 m tele- ff ∼ including the light time e ect and the ephemerides obtained once con- scope obtaining mid-transit times precisions of 6 s. Typically it sidering the intrinsic period of the planet (Eq. (4), see text). The dotted can be assumed that small or moderate groundbased telescopes line represents the accumulation over time of the difference between the can reach precisions <20 s, while large telescope may reach bet- observed period of the planet and its intrinsic period if the planet period ter than 10 s precision. Given these results we considered that is measured at the epoch t0 coincident with the origin of the x-axis, and a TTV detection threshold equal to τ = 50 s can be reasonably it is then assumed constant. Upper figure, lower panel:theO−Cdia- applied in our analysis. gram (Eq. (6)). The inner plot shows a close-up view of the O−Cdia- We randomly chose the period, mass ratio, and eccentric- gram during the first 10 years after the period determination. Units are the same of the large plot. We assumed Pbin = 172.865 years, e = 0, ity of the binary considering the probability distributions pre- ◦ q = m2/m1 = 0.23, ω = 0, i = 90 . Lower figure: graphical representa- sented in Sect. 2. The mass of the primary star was fixed at 1 M, tion of disequation 7 in function of t0, the epoch of the planetary period since we are considering binarity among typical solar type stars. determination, for the case of the orbit considered in the upper figure. The argument of the pericenter was instead randomly chosen us- The horizontal black solid lines denote the time intervals where the con- ing a uniform probability distribution. The inclination was either dition for transit timing detectability is met. The value of τ is 50 s, and ◦ fixed to 90 (to consider the case of coplanar orbits) or randomly the timescale Δ T is 10 years (see text for details). chosen using a uniform probability distribution. For each orbit (characterized by P, e, q, ω, i) we numerically solved the dis- equation (7) in function of t0 (the epoch of the planetary pe- these intervals. Then we isolated the intervals in which dise- riod determination). We subdivided the period P in 10 000 equal quation (7) changed sign, and using the secant method impos- intervals of time and evaluated disequation (7) at the extremes ing a threshold for the convergence equal to 0.1 s we obtained

Page 4 of 6 M. Montalto: Planetary transit timing variations induced by stellar binarity

Table 1. Expected frequency ( fdet) of binary stellar systems detectable by means of transit timing variations in function of the timescale (Δ T) since the discovery of the planet, and of different assumptions on the inclination of the binary stellar systems.

◦ i = 90 Δ Tfdet (yr) (%) 51.0 ± 0.2 10 2.8 ± 0.3 ◦ ◦ 0 ≤ i ≤ 90 Δ Tfdet (yr) (%) 50.6 ± 0.1 10 1.7 ± 0.2

timescales. Orbits having Pdet > 99% have also periods smaller than P < 1.67 × 105 (considering a timescale of 10 years), which means that transit timing can allow discovery of stellar compan- ions up to separations equal to a ∼ 75 AU after 10 years since the discovery of the planet (a ∼ 36 AU after 5 years). Then, considering the observed frequency of binaries in the solar surrounding with periods P > 5 × 103 days (27%) and the case of coplanar orbits, after 5 years since the discovery of a Fig. 2. Distributions of the detection probabilities (Pdet) of transit timing sample of transiting planets 1.0% ± 0.2% transiting planet host- variations of transiting planets in binary stellar systems, relative to our stars will have a probability Pdet > 99% to present detectable sample of 106 simulated binary orbits. The simulations are performed ff (>50 s) transit timing variations induced by stellar binarity, and in function of di erent time intervals since the discovery of the planets 2.8% ± 0.3% after 10 years. Considering the case of random (Δ t = 5 years or 10 years), and in function of different assumptions inclinations the expected frequencies ( fdet)are0.6% ± 0.1% and on the inclination of the binary stellar system orbit, as indicated by the ± labels in the different panels. 1.7% 0.2% after 5 and 10 years respectively. These results are summarized in Table 1. Our estimates can be considered a conservative lower limit, since we have excluded binaries with the roots of the correspondent equation. Then we determined the periods P < 5 × 103 days. intervals Δ t0 where disequation (7) was satisfied. Summing up together these intervals of time and dividing by the period of the binary gave the probability to observe the requested tran- 6. Conclusions sit timing variation for that fixed orbit over the given timescale Δ = − In this paper we have investigated how known transiting extra- ( t t t0 either 5 yr or 10 yr in our simulations) assuming solar planets can be used to constrain the frequency of multiple to determine the period of the transiting planet in correspon- stellar systems among planet-host stars. The presence of a stellar dence of a random orbital phase of the binary. In such a way companion in these systems is expected to induce transit timing we assigned to each simulated orbit a transit timing detection variations of the transiting planets even once perturbing effects probability (Pdet). In Fig. 1 (lower figure), we show the graphi- are neglected, due to the orbital revolution of the primary around cal representation of disequation (7) in function of t0, the epoch the barycenter of the binary stellar system. of the planetary period determination, for the case of the orbit If the frequency of binaries among planet-host stars is the considered in Fig. 1 (upper figure), assuming a transit timing = same as determined in the solar neighborhood, after 5 years threshold τ 50 s, and a timescale of 10 years. The horizontal since the discovery of a sample of transiting planets 1.0% ± black solid lines denote the time intervals where disequation (7) 0.2% of them have a probability >99% to present a transit tim- is satisfied. We performed 100 runs of 10 000 simulations each, ing variations >50 s induced by stellar binarity, and 2.8 ± 0.3% calculating the mean detection probabilities and their 1-σ uncer- after 10 years if the planetary and binary orbits are coplanar. tainties, as reported in the next section. Considering the case of random inclinations the probabilities are 0.6% ± 0.1% and 1.7% ± 0.2% after 5 and 10 years respectively. × 5. Results Our results have been obtained assuming a binary period P > 5 103 (a ∼> 6 AU). Moreover, we derived that we can expect to dis- The final detection probability histograms are shown in Fig. 2, cover stellar companions of transiting planets host stars up to a obtained from the entire sample of 106 simulated orbits. While maximum separations a ∼ 75 AU after 10 years since the dis- most orbits imply null detection probabilities over the assumed covery of a planet (a ∼ 36 AU after 5 years). timescales, in each one of the different situations we considered, A final comment is necessary to mention that TTVs may the histograms present a probability tail extended toward large have several different origins among which perturbing effects detection probabilities. The number of orbits having Pdet > 99% caused by additional planets or moons, secular precession due is equal to 3.9% ± 0.2% after 5 years since the period deter- to general relativity, stellar , the Appelgate effect mination (10.4% ± 0.3% after 10 years) for the case of copla- (Agol et al. 2005; Holman & Murray 2005; Veras et al. 2010; nar orbits, and is equal to 2.2% ± 0.1% after 5 years (6.2% ± Miralda-Escudé 2002;Nesvorný2009;Heyl&Gladman2007; 0.2% after 10 years) for the case of random inclinations. The Ford & Holman 2007; Simon 2007; Kipping 2009a,b; Pál & fact that the histograms are extended toward large probabili- Kocsis 2008; Rafikov 2009; Watson 2010), and binarity of the ties is a consequence of the period distribution and the adopted host is one of them. However, transit timing variations induced

Page 5 of 6 A&A 521, A60 (2010) by binarity are expected to produce long-term trends, and in par- Fischer, D. A., & Valenti, J. 2005, ApJ, 622, 1102 ticular they should be associated also with radial velocity drifts Ford, E. B., & Holman, M. J. 2007, ApJ, 664, 51 of the host star. Transit timing searchers should also follow-up Hatzes, P. A., Cochran, W. D., Endl, M., et al. 2003, ApJ, 599, 1383 Heyl, J. S., & Gladman, B. J. 2007, MNRAS, 377, 1511 spectroscopically their targets, since a transit timing variation Holman, M. J., & Murray, N. W. 2005, Science, 307, 1288 associated with a radial velocity variation will be very likely the Irwin, J. B. 1959, AJ, 64, 149 signature of binarity. Kopal, Z. 1959, Close Binary Systems, The international astrophysics series Kipping, D. M. 2009a, MNRAS, 392, 181 Kipping, D. M. 2009b, MNRAS, 396, 1797 Acknowledgements. The author is grateful to Dr. Daniel Fabrycky, Lee, J. W., Kim, S.-L., Kim, C.-H., et al. 2009, AJ, 137, 3181 Dr. Francesco Marzari, and Dr. Silvano Desidera for interesting com- Luhman, K. L., & Jayawardhana, R. 2002, ApJ, 566, 1132 ments and discussions about planets in binary stellar systems, and to the McLaughlin, D. B. 1924, ApJ, 60, 22 anonymous referee for his/her useful comments and suggestions. Marzari, F., Weidenschilling, S. J., Barbieri, M., et al. 2005, ApJ, 618, 502 Marzari, F., Thébault, P., & Scholl, H. 2009, A&A, 507, 505 Maxted, P. F. L., Anderson, D. R., Gillon, M., et al. 2010, AJ, accepted arXiv:1004.1514 References [ ] Miralda-Escudé, J. 2002, ApJ, 564, 1019 Adams, E. R., López-Morales, M., Elliot, J. L., et al. 2010, ApJ, 714, 13 Mugrauer, M., Seifahrt, A., & Neuh¨auser, R. 2007, MNRAS, 378, 1328 Agol, E., Steffen, J., Sari, R., & Clarkson, W. 2005, MNRAS, 359, 567 Nelson, A. F. 2000, ApJ, 537, 65 Artymowicz, P., & Lubow, S. H. 1994, ApJ, 421, 651 Nesvorný, D. 2009, ApJ, 701, 1116 Boss, A. P. 1997, Science, 276, 1836 Ofir, A. 2008, MNRAS, 387, 1597 Brown, T. M. 2003, ApJ, 593, 125 Pál, A., & Kocsis, B. 2008, MNRAS, 389, 191 Bonavita, M., & Desidera, S. 2007, A&A, 468, 721 Patience, J., White, R. J., Ghez, A. M., et al. 2002, ApJ, 581, 654 Chauvin, G., Lagrange, A.-M., Udry, S., et al. 2006, A&A, 456, 1165 Pfahl, E., & Muterspaugh, M. 2006, ApJ, 652, 1694 Caton, D. B., Davis, S. A., & Kluttz, K. A. 2000, in BAAS, 32, 1416 Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al. 1996, Icarus, 124, 62 Correia, A. C. M., Udry, S., Mayor, M., et al. 2008, A&A, 479, 271 Queloz, D., Mayor, M., Weber, L., et al. 2000, A&A, 354, 99 Daemgen, S., Hormuth, F., Brandner, W., et al. 2009, A&A, 498, 567 Queloz, D., Anderson, D., Collier Cameron, A., et al. 2010, A&A, 517, L1 Deeg, H. J., Doyle, L. R., Kozhevnikov, V. P., et al. 1998, A&A, 338, 479 Rabus, M., Deeg, H. J., Alonso, R., et al. 2009, A&A, 508, 1011 Deeg, H. J., Oca˜na, B., Kozhevnikov, V. P., et al. 2008, A&A, 480, 563 Rafikov, R. R. 2009, ApJ, 700, 965 Desidera, S., & Barbieri, M. 2007, A&A, 462, 345 Rossiter, R. A. 1924, ApJ, 60, 15 Doyle, L. R., & Deeg, H.-J. 2004, in Bioastronomy 2002: Life Among the Stars, Santos, N. C., Mayor, M., Naef, D., et al. 2002, A&A, 392, 215 ed. R. Norris, & F. Stootman, IAU Symp., 213, 80 Schnupp, C., Bergfors, C., Brandner, W., et al. 2010, A&A, 516, A21 Doyle, L. R., Deeg, H. J., Kozhevnikov, V. P., et al. 2000, ApJ, 535, 338 Simon, A., Szatmáry, K., & Szabó, Gy. M. 2007, A&A, 470, 727 Duchêne, G. 2010, ApJ, 709, 114 Watson, C. A., & Marsh, T. R. 2010, MNRAS, 405, 2037 Duquennoy, A., & Mayor, M. 1991, A&A, 248, 485 Triaud, A. H. M. J., Collier Cameron, A., Queloz, D., et al. 2010, A&A, Eggenberger, A., & Udry, S. 2007 [arXiv:0705.3173] in press Eggenberger, A., Udry, S., Chauvin, G., et al. 2007, A&A, 474, 273 Veras, D., Ford, E. B., & Payne, M. J. 2010, ApJ, submitted Eggenberger, A., Udry, S., Chauvin, G., et al. 2008, ASPC, 398, 179 Winn, J. N., Mattew, J. H., Joshua, A. C., et al. 2009, AJ, 137, 3826 Els, S. G., Sterzik, M. F., Marchis, F., et al. 2001, A&A, 370, 1 Winn, J. N., Johnson, J. A., Howard, A. W., et al. 2010, ApJ, 718, 575

Page 6 of 6